Convergence Of Time Space Discontinuous Fully Discrete Finite Element For One-order Hyperbolic System

Basing on the discontinuous finite element ideal for ordinary differential,we have taken advantage of energy method , orthogonal analysis in element,construct especial orthogonal analyze and tensor product decompose,simply prove convergence of space-time discontinuous finite element of one-order hyperbolic system.We have had full-degree error estimation .Numerical experimentation have not only proved the theoretical result but also found out superconvergence of higher order.Main result follows:(1)According to the ideal of R-orthogonal expand , tensor product decompose and the method of energy ,we have simply proved one-order hyperbolic systems problem time-space discontinuous finite element solution U ∈ S~k(?)S~h(for time space o,1 degree,space m-degree)have full-degree convergence:||(u - U)|| ≤ C(T,u)(h~m+1 + k~p+1)Where S~k is p-degree finite element space in time,S~h is m-degree finite element space in space.This method is good for multiplicity-dimension too.(2)Professor Chuanmiao Chen has proved superconvergence at p+ 1-order Radau points in the element.At the first time,numerical experimentation prove has similar superconvergence at p + 1 and k 4- 1-degree Radau points' product points for one-order hyperbolic problem by using discontinuous finite element method.But the result has not been proved in theory yet.